A $$1,000$ bond has a coupon of $6$ percent and matures after $10$ years.

a$.$ What would be the bond's price if comparable debt yields $8$ percent?

b$.$ What would be the price if comparable debt yields $8$ percent and the bond

matures after five years?

c$.$ Why are the prices different in questions $($a$)$ and $($b$)?$

d$.$ What are the current yields and the yields to maturity in questions $($a$)$ and

$($b$)?$

e$.$ If interest rates increase $100$ basis points $($that is$,$ from $8$ percent to $9$ percent$),$

what are the new prices of both bonds assuming annual compounding?

a$.$ Calculate the percentage change in the price of each bond and, based on this

information, identify which has the higher duration.